The algebraic rigidity of BCH codes challenges the development of parallelizable and efficient decoders for high-throughput applications. To address this, we propose a hybrid scheme combining normalized min-sum and order statistics decoding, achieving near-maximum likelihood performance for short BCH codes while retaining the benefits of the normalized min-sum decoder over a wide SNR range. First, a heuristic method constructs a parity-check matrix with low density, appropriate redundancy, and fewer length-4 cycles through binary sum and random row cyclic shifts, forming a solid foundation for decoder design. The impact of row redundancy and rank deficiency in the dual code's minimum-weight codewords on frame error rate is analyzed. In the revised normalized min-sum decoder, three types of random automorphisms enhance decoding diversity, while aggregated messages accelerate convergence. For BCH codes of length 63 and 127, the proposed approach achieves a 1-2 dB bit error rate advantage over parallelizable alternatives or requires up to two orders of magnitude fewer iterations than other iterative rivals. These results highlight its effectiveness in hybrid decoding for ultra-reliable, low-latency communications.

翻译：BCH码的代数刚性对高吞吐量应用中可并行化高效解码器的开发提出了挑战。为此，我们提出了一种结合归一化最小和与阶统计解码的混合方案，在宽信噪比范围内保持归一化最小和解码器优点的同时，为短BCH码实现了接近最大似然的性能。首先，通过二进制求和与随机行循环移位，一种启发式方法构建了具有低密度、适当冗余和较少长度为4环的奇偶校验矩阵，为解码器设计奠定了坚实基础。分析了双码最小重量码字中行冗余和秩亏缺对帧错误率的影响。在改进的归一化最小和解码器中，三类随机自同构增强了解码多样性，而聚合消息则加速了收敛。对于长度为63和127的BCH码，所提方案在比特错误率上比可并行化替代方案获得1-2 dB优势，或所需迭代次数比其他迭代竞争方案少达两个数量级。这些结果凸显了其在超可靠低延迟通信混合解码中的有效性。